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mvar writes "On Feb. 6th, NASA's twin STEREO probes moved into position on opposite sides of the sun, and they are now beaming back uninterrupted images of the entire star—front and back. 'For the first time ever, we can watch solar activity in its full 3-dimensional glory,' says Angelos Vourlidas, a member of the STEREO science team at the Naval Research Lab in Washington, DC. NASA released a 'first light' 3D movie on, naturally, Super Bowl Sunday."

STEREO, as the name suggests, has been broadcasting 3D images of the sun since it launched many, many years ago. the satellites had slightly (and increasingly) different viewpoints, which could then be combined to give a binocular view of the sun. The long-term mission was to put the satellites at opposite sides of the sun for continuous coverage of the surface, a position in which they cannot generate 3D images of it because their perspectives are completely exclusive. That is what has been achieved.

Very. You'd have to fight gravity with propulsion or they would fall into the object. A satellite has to orbit or it will fall into the planet.

You could get fancy and try to exploit another object's gravity and then occupy the Lagrangian points, but I can't think of a real-world example of where this would work at the poles.

If you used an extremely elliptical orbit, you could at least have a line-of-sight to a pole for a long period of time. Use two satellites and you could cover a pole full-time using an elliptical orbit.